Global $+$-regularity of regular del Pezzo surfaces in mixed characteristic

Hirotaka Onuki

Global $+$-regularity of regular del Pezzo surfaces in mixed characteristic

Algebraic Geometry 2026-01-22 v1

Authors: Hirotaka Onuki

Abstract

Let $R = W(k)$ be the ring of Witt vectors over an algebraically closed field $k$ of characteristic $p > 2$ . Let $M$ be a three-dimensional regular integral flat projective $R$ -scheme such that $H^0(M,\mathcal{O}_M) = R$ and the anticanonical sheaf $\omega_M^{-1}$ is ample. We show that $M$ is globally $+$ -regular if the closed fiber $M_k$ is reduced.

Keywords

del Pezzo surface global $+$-regularity mixed characteristic Witt vectors anticanonical sheaf

Cite

@article{arxiv.2601.15270,
  title  = {Global $+$-regularity of regular del Pezzo surfaces in mixed characteristic},
  author = {Hirotaka Onuki},
  journal= {arXiv preprint arXiv:2601.15270},
  year   = {2026}
}

Comments

23 pages

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